Accurate experimental values for the vibrational ground tone or fundamental vibrational energy splitting of H$_2$, HD, and D$_2$ are presented. Absolute accuracies of $2\times10^{ -4}$ cm$^{ -1}$ are obtained from Doppler-free laser spectroscopy applied in a collisionless environment. The vibrational splitting frequencies are derived from the combination difference between separate electronic excitations from the $X^{ 1}\Sigma_{ g}^{ +}, v=0, J$ and $v=1, J$ vibrational states to a common $EF^{ 1}\Sigma^{ +}_{ g}, v=0, J$ state. The present work on rotational quantum states $J=1,2$ extends the results reported by Dickenson et al. on $J=0$ [Phys. Rev. Lett. 110 (2013) 193601]. The experimental procedures leading to this high accuracy are discussed in detail. A comparison is made with full \emph{ ab initio} calculations encompassing Born-Oppenheimer energies, adiabatic and non-adiabatic corrections, as well as relativistic corrections and QED-contributions. The present agreement between the experimental results and the calculations provides a stringent test on the application of quantum electrodynamics in molecules. Furthermore, the combined experimental-theoretical uncertainty can be interpreted to provide bounds to new interactions beyond the Standard Model of Physics or fifth forces between hadrons.
Categories: physics.atom-ph